Ellipse questions
211 published questions with worked solutions.
- Let a, b and be positive real numbers. Suppose P is an end point of the latus rectum of the parabola y^2 = 4 x, and suppose the...
- Consider the ellipse x^2 4 + y^2 3 = 1. Let H( , 0), 0 < < 2, be a point. A straight line drawn through H parallel to the y-axis...
- Consider the ellipse x^2 9 + y^2 4 = 1. Let S(p, q) be a point in the first quadrant such that p^2 9 + q^2 4 > 1. Two tangents...
- An ellipse E : x^ 2 /a^ 2 + y^ 2 /b^ 2 = 1 passes through the vertices of the hyperbola H : x^ 2 /49 - y^ 2 /64 = −1. Let the...
- If the length of the latus rectum of the ellipse x^ 2 + 4y^ 2 + 2x + 8y - = 0, is 4 and is the length of its major axis, then +...
- Let the eccentricity of an ellipse x^ 2 /a^ 2 + y^ 2 /b^ 2 = 1, a > b, be 1/4. If this ellipse passes through the point (-4 2/5 ,...
- Let the tangents at points P and Q on the ellipse x^ 2 /2 + y^ 2 /4 = 1 meet at the point R( 2 , 2 2 - 2). If S is the focus of...
- Let a line L pass through the point of intersection of the lines bx + 10y − 8 = 0 and 2x − 3y = 0, b R − 4/3 . If the line L also...
- The sum of the focal distances of a point on an ellipse is constant and equal to the
- Let P(x_1, y_1) and Q(x_2, y_2) be two distinct points on the ellipse x^2 9 + y^2 4 = 1 such that y_1 > 0, and y_2 > 0. Let C...
- Let a circle of radius 4 be concentric to the ellipse 15x^2+19y^2=285. Then the common tangents are inclined to the minor axis of...
- Let the ellipse E: x^2+9y^2=9 intersect the positive x- and y-axes at the points A and B respectively. Let the major axis of E be...
- Consider ellipses E_k: kx^2+k^2y^2=1, k = 1, 2,…,20. Let C_k be the circle which touches the four chords joining the end points...
- Let P ( 2 3 7 , 6 7 ), Q, R and S be four points on the ellipse 9x^2+4y^2=36. Let PQ and RS be mutually perpendicular and pass...
- Let an ellipse with center (1, 0) and latus rectum of length 1 2 have its major axis along x-axis. If its minor axis subtends an...
- The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x^2 + 9y^2 = 9 meets...
- An ellipse intersects the hyperbola 2x^2 - 2y^2 = 1 orthogonally. The eccentricity of the ellipse is reciprocal of that of the...
- The foci of the ellipse x^2 16 + y^2 b^2 = 1 and the hyperbola x^2 144 - y^2 81 = 1 25 coincide. Then the value of b^2 is
- The eccentricity of an ellipse, with its centre at the origin, is 1 2 . If one of the directrices is x = 4 , then the equation of...
- An ellipse has OB as semi minor axis, F and F′ its focii and the angle FBF′ is a right angle. Then the eccentricity of the...
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